Abstract

Immersion lithography systems with hyper-numerical aperture (hyper-NA) (NA>1) have become indispensable in nanolithography for technology nodes of 45 nm and beyond. Source and mask optimization (SMO) has emerged as a key technique used to further improve the imaging performance of immersion lithography. Recently, a set of pixelated gradient-based SMO approaches were proposed under the scalar imaging models, which are inaccurate for hyper-NA settings. This paper focuses on developing pixelated gradient-based SMO algorithms based on a vector imaging model that is accurate for current immersion lithography. To achieve this goal, an integrative and analytic vector imaging model is first used to formulate the simultaneous SMO (SISMO) and sequential SMO (SESMO) frameworks. A gradient-based algorithm is then exploited to jointly optimize the source and mask. Subsequently, this paper studies and compares the performance of individual source optimization (SO), individual mask optimization (MO), SISMO, and SESMO. Finally, a hybrid SMO (HSMO) approach is proposed to take full advantage of SO, SISMO, and MO, consequently achieving superior performance.

© 2012 Optical Society of America

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2012 (1)

2011 (6)

X. Ma and Y. Li, “Resolution enhancement optimization methods in optical lithography with improved manufacturability,” J. Microlith. Microfab. Microsyst. 10(2), 023009 (2011).
[CrossRef]

Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical lithography,” IEEE Trans. Image Process. 20, 2856–2864 (2011).
[CrossRef]

J. Yu and P. Yu, “Gradient-based fast source mask optimization (SMO),” Proc. SPIE 7973, 797320 (2011).
[CrossRef]

N. Jia and E. Y. Lam, “Pixelated source mask optimization for process robustness in optical lithography,” Opt. Express 19, 19384–19398 (2011).
[CrossRef]

X. Ma and G. R. Arce, “Pixel-based OPC optimization based on conjugate gradients,” Opt. Express 19, 2165–2180 (2011).
[CrossRef]

X. Ma, G. R. Arce, and Y. Li, “Optimal 3D phase-shifting masks in partially coherent illumination,” Appl. Opt. 50, 5567–5576 (2011).
[CrossRef]

2010 (4)

J. Yu and P. Yu, “Impacts of cost functions on inverse lithography patterning,” Opt. Express 18, 23331–23342 (2010).
[CrossRef]

Y. V. Miklyaev, W. Imgrunt, V. S. Pavelyev, D. G. Kachalov, T. Bizjak, L. Aschke, and V. N. Lissotschenko, “Novel continuously shaped diffractive optical elements enable high-efficiency beam shaping,” Proc. SPIE 7640, 7640–7674 (2010).
[CrossRef]

J. T. Carriere, J. Stack, A. D. Kathman, and M. D. Himel, “Advances in doe modeling and optical performance for SMO applications in immersion lithography at the 32 nm node and beyond,” Proc. SPIE 7640, 7640–7675 (2010).
[CrossRef]

D. Peng, P. Hu, V. Tolani, and T. Dam, “Toward a consistent and accurate approach to modeling projection optics,” Proc. SPIE 7640, 76402Y (2010).
[CrossRef]

2009 (3)

X. Ma and G. R. Arce, “Pixel-based simultaneous source and mask optimization for resolution enhancement in optical lithography,” Opt. Express 17, 5783–5793 (2009).
[CrossRef]

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Y. Shen, N. Wong, and E. Y. Lam, “Level-set-based inverse lithography for photomask synthesis,” Opt. Express 17, 23690–23701 (2009).
[CrossRef]

2008 (4)

2007 (2)

A. Poonawala and P. Milanfar, “Fast and low-complexity mask design in optical microlithography—an inverse imaging problem,” IEEE Trans. Image Process. 16, 774–788 (2007).
[CrossRef]

X. Ma and G. R. Arce, “Generalized inverse lithography methods for phase-shifting mask design,” Opt. Express 15, 15066–15079 (2007).
[CrossRef]

2006 (1)

A. Poonawala and P. Milanfar, “OPC and PSM design using inverse lithography: a non-linear optimization approach,” Proc. SPIE 6154, 1159–1172 (2006).
[CrossRef]

2005 (3)

C. Progler, W. Conley, B. Socha, and Y. Ham, “Layout and source dependent phase mask transmission tuning,” Proc. SPIE 5454, 315–326 (2005).
[CrossRef]

S. Robert, X. Shi, and L. David, “Simultaneous source mask optimization (SMO),” Proc. SPIE 5853, 180–193 (2005).
[CrossRef]

M. Totzeck, P. Graüpner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, “Polarization influence on imaging,” J. Microlith. Microfab. Microsyst. 4, 031108 (2005).
[CrossRef]

2002 (1)

A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. Molless, R. N. Singh, and A. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. Microsyst. 1, 13–30 (2002).
[CrossRef]

2001 (1)

2000 (1)

T. V. Pistor, A. R. Neureuther, and R. J. Socha, “Modeling oblique incidence effects in photomasks,” Proc. SPIE 4000, 228–237 (2000).
[CrossRef]

1995 (1)

S. Sherif, B. Saleh, and R. Leone, “Binary image synthesis using mixed integer programming,” IEEE Trans. Image Process. 4, 1252–1257 (1995).
[CrossRef]

1992 (1)

Y. Liu and A. Zakhor, “Binary and phase shifting mask design for optical lithography,” IEEE Trans. Semicond. Manuf. 5, 138–152 (1992).
[CrossRef]

1982 (1)

M. D. Levenson, N. S. Viswanathan, and R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron. Devices ED-29, 1828–1836(1982).
[CrossRef]

Arce, G. R.

Aschke, L.

Y. V. Miklyaev, W. Imgrunt, V. S. Pavelyev, D. G. Kachalov, T. Bizjak, L. Aschke, and V. N. Lissotschenko, “Novel continuously shaped diffractive optical elements enable high-efficiency beam shaping,” Proc. SPIE 7640, 7640–7674 (2010).
[CrossRef]

Azpiroz, J. T.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Bagheri, S.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Bizjak, T.

Y. V. Miklyaev, W. Imgrunt, V. S. Pavelyev, D. G. Kachalov, T. Bizjak, L. Aschke, and V. N. Lissotschenko, “Novel continuously shaped diffractive optical elements enable high-efficiency beam shaping,” Proc. SPIE 7640, 7640–7674 (2010).
[CrossRef]

Bukofsky, S.

A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. Molless, R. N. Singh, and A. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. Microsyst. 1, 13–30 (2002).
[CrossRef]

Burkhardt, M.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Burr, G.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Callan, N.

S. Hsu, L. Chen, Z. Li, S. Park, K. Gronlund, H. Liu, N. Callan, R. Socha, and S. Hansen, “An innovative source-mask co-optimization (SMO) method for extending low k1 imaging,” Proc. SPIE 7140, 714010 (2008).
[CrossRef]

Carpaij, R.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Carriere, J. T.

J. T. Carriere, J. Stack, A. D. Kathman, and M. D. Himel, “Advances in doe modeling and optical performance for SMO applications in immersion lithography at the 32 nm node and beyond,” Proc. SPIE 7640, 7640–7675 (2010).
[CrossRef]

Chan, S. H.

Chen, L.

S. Hsu, L. Chen, Z. Li, S. Park, K. Gronlund, H. Liu, N. Callan, R. Socha, and S. Hansen, “An innovative source-mask co-optimization (SMO) method for extending low k1 imaging,” Proc. SPIE 7140, 714010 (2008).
[CrossRef]

Conley, W.

C. Progler, W. Conley, B. Socha, and Y. Ham, “Layout and source dependent phase mask transmission tuning,” Proc. SPIE 5454, 315–326 (2005).
[CrossRef]

Corliss, D.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Dam, T.

D. Peng, P. Hu, V. Tolani, and T. Dam, “Toward a consistent and accurate approach to modeling projection optics,” Proc. SPIE 7640, 76402Y (2010).
[CrossRef]

David, L.

S. Robert, X. Shi, and L. David, “Simultaneous source mask optimization (SMO),” Proc. SPIE 5853, 180–193 (2005).
[CrossRef]

Dittmann, O.

M. Totzeck, P. Graüpner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, “Polarization influence on imaging,” J. Microlith. Microfab. Microsyst. 4, 031108 (2005).
[CrossRef]

Dong, L.

Engelen, A.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Fakhry, M.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Faure, T.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Flagello, D.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

M. Totzeck, P. Graüpner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, “Polarization influence on imaging,” J. Microlith. Microfab. Microsyst. 4, 031108 (2005).
[CrossRef]

Fonseca, C.

A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. Molless, R. N. Singh, and A. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. Microsyst. 1, 13–30 (2002).
[CrossRef]

Gallagher, E.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Gallatin, G. M.

Göhnermeier, A.

M. Totzeck, P. Graüpner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, “Polarization influence on imaging,” J. Microlith. Microfab. Microsyst. 4, 031108 (2005).
[CrossRef]

Goodman, J.

J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill Science, 1996).

Graüpner, P.

M. Totzeck, P. Graüpner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, “Polarization influence on imaging,” J. Microlith. Microfab. Microsyst. 4, 031108 (2005).
[CrossRef]

Groenendijk, R.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Gronlund, K.

S. Hsu, L. Chen, Z. Li, S. Park, K. Gronlund, H. Liu, N. Callan, R. Socha, and S. Hansen, “An innovative source-mask co-optimization (SMO) method for extending low k1 imaging,” Proc. SPIE 7140, 714010 (2008).
[CrossRef]

Hageman, J.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Halle, S.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Ham, Y.

C. Progler, W. Conley, B. Socha, and Y. Ham, “Layout and source dependent phase mask transmission tuning,” Proc. SPIE 5454, 315–326 (2005).
[CrossRef]

Hansen, S.

S. Hsu, L. Chen, Z. Li, S. Park, K. Gronlund, H. Liu, N. Callan, R. Socha, and S. Hansen, “An innovative source-mask co-optimization (SMO) method for extending low k1 imaging,” Proc. SPIE 7140, 714010 (2008).
[CrossRef]

Hartung, F.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Heil, T.

M. Totzeck, P. Graüpner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, “Polarization influence on imaging,” J. Microlith. Microfab. Microsyst. 4, 031108 (2005).
[CrossRef]

Hennerkes, C.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Hibbs, M.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. Molless, R. N. Singh, and A. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. Microsyst. 1, 13–30 (2002).
[CrossRef]

Himel, M. D.

J. T. Carriere, J. Stack, A. D. Kathman, and M. D. Himel, “Advances in doe modeling and optical performance for SMO applications in immersion lithography at the 32 nm node and beyond,” Proc. SPIE 7640, 7640–7675 (2010).
[CrossRef]

Hoffnagle, J.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Hsu, S.

S. Hsu, L. Chen, Z. Li, S. Park, K. Gronlund, H. Liu, N. Callan, R. Socha, and S. Hansen, “An innovative source-mask co-optimization (SMO) method for extending low k1 imaging,” Proc. SPIE 7140, 714010 (2008).
[CrossRef]

Hu, P.

D. Peng, P. Hu, V. Tolani, and T. Dam, “Toward a consistent and accurate approach to modeling projection optics,” Proc. SPIE 7640, 76402Y (2010).
[CrossRef]

Imgrunt, W.

Y. V. Miklyaev, W. Imgrunt, V. S. Pavelyev, D. G. Kachalov, T. Bizjak, L. Aschke, and V. N. Lissotschenko, “Novel continuously shaped diffractive optical elements enable high-efficiency beam shaping,” Proc. SPIE 7640, 7640–7674 (2010).
[CrossRef]

Jia, N.

N. Jia and E. Y. Lam, “Pixelated source mask optimization for process robustness in optical lithography,” Opt. Express 19, 19384–19398 (2011).
[CrossRef]

N. Jia and E. Y. Lam, “Performance analysis of pixelated source-mask optimization for optical microlithography,” in Proceedings of IEEE International Conference of Electron Devices and Solid-State Circuits (EDSSC) (IEEE, 2010).

Kachalov, D. G.

Y. V. Miklyaev, W. Imgrunt, V. S. Pavelyev, D. G. Kachalov, T. Bizjak, L. Aschke, and V. N. Lissotschenko, “Novel continuously shaped diffractive optical elements enable high-efficiency beam shaping,” Proc. SPIE 7640, 7640–7674 (2010).
[CrossRef]

Kamenov, V.

M. Totzeck, P. Graüpner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, “Polarization influence on imaging,” J. Microlith. Microfab. Microsyst. 4, 031108 (2005).
[CrossRef]

Kathman, A. D.

J. T. Carriere, J. Stack, A. D. Kathman, and M. D. Himel, “Advances in doe modeling and optical performance for SMO applications in immersion lithography at the 32 nm node and beyond,” Proc. SPIE 7640, 7640–7675 (2010).
[CrossRef]

Kazinczi, R.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Kim, Y.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Kneer, B.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Krähmer, D.

M. Totzeck, P. Graüpner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, “Polarization influence on imaging,” J. Microlith. Microfab. Microsyst. 4, 031108 (2005).
[CrossRef]

Lai, K.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. Molless, R. N. Singh, and A. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. Microsyst. 1, 13–30 (2002).
[CrossRef]

Lam, E. Y.

Leone, R.

S. Sherif, B. Saleh, and R. Leone, “Binary image synthesis using mixed integer programming,” IEEE Trans. Image Process. 4, 1252–1257 (1995).
[CrossRef]

Levenson, M. D.

M. D. Levenson, N. S. Viswanathan, and R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron. Devices ED-29, 1828–1836(1982).
[CrossRef]

Li, Y.

Li, Z.

S. Hsu, L. Chen, Z. Li, S. Park, K. Gronlund, H. Liu, N. Callan, R. Socha, and S. Hansen, “An innovative source-mask co-optimization (SMO) method for extending low k1 imaging,” Proc. SPIE 7140, 714010 (2008).
[CrossRef]

Lissotschenko, V. N.

Y. V. Miklyaev, W. Imgrunt, V. S. Pavelyev, D. G. Kachalov, T. Bizjak, L. Aschke, and V. N. Lissotschenko, “Novel continuously shaped diffractive optical elements enable high-efficiency beam shaping,” Proc. SPIE 7640, 7640–7674 (2010).
[CrossRef]

Liu, H.

S. Hsu, L. Chen, Z. Li, S. Park, K. Gronlund, H. Liu, N. Callan, R. Socha, and S. Hansen, “An innovative source-mask co-optimization (SMO) method for extending low k1 imaging,” Proc. SPIE 7140, 714010 (2008).
[CrossRef]

Liu, Y.

Y. Liu and A. Zakhor, “Binary and phase shifting mask design for optical lithography,” IEEE Trans. Semicond. Manuf. 5, 138–152 (1992).
[CrossRef]

Ma, X.

Maul, M.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

McIntyre, G.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Melville, D.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Miklyaev, Y. V.

Y. V. Miklyaev, W. Imgrunt, V. S. Pavelyev, D. G. Kachalov, T. Bizjak, L. Aschke, and V. N. Lissotschenko, “Novel continuously shaped diffractive optical elements enable high-efficiency beam shaping,” Proc. SPIE 7640, 7640–7674 (2010).
[CrossRef]

Milanfar, P.

A. Poonawala and P. Milanfar, “Fast and low-complexity mask design in optical microlithography—an inverse imaging problem,” IEEE Trans. Image Process. 16, 774–788 (2007).
[CrossRef]

A. Poonawala and P. Milanfar, “OPC and PSM design using inverse lithography: a non-linear optimization approach,” Proc. SPIE 6154, 1159–1172 (2006).
[CrossRef]

Molless, A.

A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. Molless, R. N. Singh, and A. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. Microsyst. 1, 13–30 (2002).
[CrossRef]

Neureuther, A. R.

T. V. Pistor, A. R. Neureuther, and R. J. Socha, “Modeling oblique incidence effects in photomasks,” Proc. SPIE 4000, 228–237 (2000).
[CrossRef]

Park, S.

S. Hsu, L. Chen, Z. Li, S. Park, K. Gronlund, H. Liu, N. Callan, R. Socha, and S. Hansen, “An innovative source-mask co-optimization (SMO) method for extending low k1 imaging,” Proc. SPIE 7140, 714010 (2008).
[CrossRef]

Pavelyev, V. S.

Y. V. Miklyaev, W. Imgrunt, V. S. Pavelyev, D. G. Kachalov, T. Bizjak, L. Aschke, and V. N. Lissotschenko, “Novel continuously shaped diffractive optical elements enable high-efficiency beam shaping,” Proc. SPIE 7640, 7640–7674 (2010).
[CrossRef]

Peng, D.

D. Peng, P. Hu, V. Tolani, and T. Dam, “Toward a consistent and accurate approach to modeling projection optics,” Proc. SPIE 7640, 76402Y (2010).
[CrossRef]

Peng, Y.

Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical lithography,” IEEE Trans. Image Process. 20, 2856–2864 (2011).
[CrossRef]

Pistor, T. V.

T. V. Pistor, A. R. Neureuther, and R. J. Socha, “Modeling oblique incidence effects in photomasks,” Proc. SPIE 4000, 228–237 (2000).
[CrossRef]

Poonawala, A.

A. Poonawala and P. Milanfar, “Fast and low-complexity mask design in optical microlithography—an inverse imaging problem,” IEEE Trans. Image Process. 16, 774–788 (2007).
[CrossRef]

A. Poonawala and P. Milanfar, “OPC and PSM design using inverse lithography: a non-linear optimization approach,” Proc. SPIE 6154, 1159–1172 (2006).
[CrossRef]

Progler, C.

C. Progler, W. Conley, B. Socha, and Y. Ham, “Layout and source dependent phase mask transmission tuning,” Proc. SPIE 5454, 315–326 (2005).
[CrossRef]

Robert, S.

S. Robert, X. Shi, and L. David, “Simultaneous source mask optimization (SMO),” Proc. SPIE 5853, 180–193 (2005).
[CrossRef]

Rohmund, F.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Rosenbluth, A. E.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. Molless, R. N. Singh, and A. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. Microsyst. 1, 13–30 (2002).
[CrossRef]

Ruoff, J.

M. Totzeck, P. Graüpner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, “Polarization influence on imaging,” J. Microlith. Microfab. Microsyst. 4, 031108 (2005).
[CrossRef]

Russ, C.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Saleh, B.

S. Sherif, B. Saleh, and R. Leone, “Binary image synthesis using mixed integer programming,” IEEE Trans. Image Process. 4, 1252–1257 (1995).
[CrossRef]

Shen, Y.

Sherif, S.

S. Sherif, B. Saleh, and R. Leone, “Binary image synthesis using mixed integer programming,” IEEE Trans. Image Process. 4, 1252–1257 (1995).
[CrossRef]

Shi, X.

S. Robert, X. Shi, and L. David, “Simultaneous source mask optimization (SMO),” Proc. SPIE 5853, 180–193 (2005).
[CrossRef]

Simpson, R. A.

M. D. Levenson, N. S. Viswanathan, and R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron. Devices ED-29, 1828–1836(1982).
[CrossRef]

Singh, R. N.

A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. Molless, R. N. Singh, and A. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. Microsyst. 1, 13–30 (2002).
[CrossRef]

Socha, B.

C. Progler, W. Conley, B. Socha, and Y. Ham, “Layout and source dependent phase mask transmission tuning,” Proc. SPIE 5454, 315–326 (2005).
[CrossRef]

Socha, R.

S. Hsu, L. Chen, Z. Li, S. Park, K. Gronlund, H. Liu, N. Callan, R. Socha, and S. Hansen, “An innovative source-mask co-optimization (SMO) method for extending low k1 imaging,” Proc. SPIE 7140, 714010 (2008).
[CrossRef]

Socha, R. J.

T. V. Pistor, A. R. Neureuther, and R. J. Socha, “Modeling oblique incidence effects in photomasks,” Proc. SPIE 4000, 228–237 (2000).
[CrossRef]

Stack, J.

J. T. Carriere, J. Stack, A. D. Kathman, and M. D. Himel, “Advances in doe modeling and optical performance for SMO applications in immersion lithography at the 32 nm node and beyond,” Proc. SPIE 7640, 7640–7675 (2010).
[CrossRef]

Tian, K.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Tolani, V.

D. Peng, P. Hu, V. Tolani, and T. Dam, “Toward a consistent and accurate approach to modeling projection optics,” Proc. SPIE 7640, 76402Y (2010).
[CrossRef]

Totzeck, M.

M. Totzeck, P. Graüpner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, “Polarization influence on imaging,” J. Microlith. Microfab. Microsyst. 4, 031108 (2005).
[CrossRef]

Viswanathan, N. S.

M. D. Levenson, N. S. Viswanathan, and R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron. Devices ED-29, 1828–1836(1982).
[CrossRef]

Wagner, A.

K. Lai, A. E. Rosenbluth, S. Bagheri, J. Hoffnagle, K. Tian, D. Melville, J. T. Azpiroz, M. Fakhry, Y. Kim, S. Halle, G. McIntyre, A. Wagner, G. Burr, M. Burkhardt, D. Corliss, E. Gallagher, T. Faure, M. Hibbs, D. Flagello, J. Zimmermann, B. Kneer, F. Rohmund, F. Hartung, C. Hennerkes, M. Maul, R. Kazinczi, A. Engelen, R. Carpaij, R. Groenendijk, J. Hageman, and C. Russ, “Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22 nm logic lithography process,” Proc. SPIE 7274, 72740A (2009).
[CrossRef]

Wang, Y.

Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical lithography,” IEEE Trans. Image Process. 20, 2856–2864 (2011).
[CrossRef]

Wong, A. K.

S. H. Chan, A. K. Wong, and E. Y. Lam, “Initialization for robust inverse synthesis of phase-shifing masks in optical projection lithography,” Opt. Express 16, 14746–14760 (2008).
[CrossRef]

A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. Molless, R. N. Singh, and A. K. Wong, “Optimum mask and source patterns to print a given shape,” J. Microlith. Microfab. Microsyst. 1, 13–30 (2002).
[CrossRef]

A. K. Wong, Resolution Enhancement Techniques in Optical Lithography (SPIE, 2001).

Wong, N.

Yu, J.

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[CrossRef]

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Appl. Opt. (2)

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Figures (7)

Fig. 1.
Fig. 1.

Intensity distribution comparison of a 45 nm line-space pattern along the Y-axis calculated by the scalar imaging model, the vector imaging model, and Prolith software under the vector model, where the binary mask and X-polarization are used.

Fig. 2.
Fig. 2.

Imaging formation based on the vector model.

Fig. 3.
Fig. 3.

Flow charts of (a) SISMO, (b) SESMO, and (c) HSMO.

Fig. 4.
Fig. 4.

Simulation comparison among individual SO, individual MO, and SMO approaches for the line-space pattern using 150 iterations. Left to right: the source patterns, mask patterns, and printed images on the wafer. Top to bottom: simulations for the initial source and mask patterns, individual SO, individual MO, SISMO, SESMO, and HSMO.

Fig. 5.
Fig. 5.

PAE convergence for individual SO, individual MO, and SMO approaches. Left column shows the PAE convergence of the line-space pattern with (a) 150 iterations, (c) 200 iterations, and (e) 250 iterations, respectively. Right column shows the PAE convergence of the complex pattern with (b) 150 iterations, (d) 200 iterations, and (f) 250 iterations, respectively. The magenta square-dashed curve, blue dashed curve, green dash-dotted curve, red dotted curve, and black solid curve represent the PAE convergence for individual SO, individual MO, SISMO, SESMO, and HSMO, respectively.

Fig. 6.
Fig. 6.

Simulations of the SISMO algorithm for the line-space pattern with different CDs. Top to bottom: the CDs of the target patterns are 45, 40, and 35 nm, respectively. Left to right: the source patterns, mask patterns, and printed images on the wafer.

Fig. 7.
Fig. 7.

Simulation comparison among individual SO, individual MO, and SMO approaches for the complex pattern using 150 iterations. Left to right: the source patterns, mask patterns, and printed images on the wafer. Top to bottom: simulations for the initial source and mask patterns, individual SO, individual MO, SISMO, SESMO, and HSMO.

Tables (2)

Tables Icon

Table 1. Error Performance, Runtimes and Trapezoid Counts of the Simulations with 150 Iterations for Initial Source and Mask Patterns, Individual SO, Individual MO, SISMO, SESMO, and HSMOa

Tables Icon

Table 2. Error Performance of the Simulations with 200 and 250 Iterations for Initial Source and Mask Patterns, Individual SO, Individual MO, SISMO, SESMO, and HSMOa

Equations (21)

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Ewafer(xs,ys)=2πnwR×(F1{V}(BM)),
Epwafer(xs,ys)=Hp(BM),p=x,y,z,
Hp=2πnwRF1{Vp}
I(xs,ys)=1JsumJ(xs,ys)p=x,y,zHp(BM)22,
I=1Jsumxsys(J(xs,ys)p=x,y,zHpxsys(BxsysM)22).
sig(x)=11+exp[a(xtr)],
Z=T{J,M}=sig{1JsumxsysJ(xs,ys)p=x,y,zHpxsys(BxsysM)22}.
F=d(Z,Z˜)=d(T{J,M},Z˜)
(J^,M^)=argminJRNs×Ns,MRN×Nd(T{J,M},Z˜).
J=f(ΩS)=1+cosΩS2;M=f(ΩM)=1+cosΩM2,
FΩS(xs,ys)=2aJsumf(ΩS(xs,ys))×1N×1T[(p=x,y,zEpwafer(xs,ys)22)(Z˜Z)Z(1Z)]1N×1,
F(ΩM)=4aJsumf(ΩM)xsys[J(xs,ys)p=x,y,zReal((Bxsys)*{(Hpxsys)*[Epwafer(xs,ys)(Z˜Z)Z(1Z)]})],
ΩSk+1=ΩSksΩSF(ΩS);ΩMk+1=ΩMksΩMF(ΩM),
M^d=Γ(M^tm),
Zb=Γ{(1JsumxsysJ(xs,ys)p=x,y,zHpxsys(BxsysMd)22)tr},
PAE=Z˜Zb22=Z˜Γ{(1JsumxsysJ(xs,ys)p=x,y,zHpxsys(BxsysMd)22)tr}22.
Epwafer(xs,ys)=F1{2πnwRVpxsysF(BxsysM)}.
F(ΩM)=4aJsumf(ΩM)xsysJ(xs,ys)p=x,y,zReal[(Bxsys)*F1{2πnwRVpxsys*CF[Epwafer(xs,ys)(Z˜Z)Z(1Z)]}],
RS=xsyssig{J(xs,ys)},
F=F+γSRS,
RS(ΩS)=a2sig{J}(1sig{J})sinΩS.

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